The argument with stem cell research is that when using 'embryonic' stem cells, we are actually killing a live developing being. The embryo is actually developing into a human being. However, the use of stem cells in umbilical cord blood is not considered unethical.
Stem cells are basically cells that will form into whatever it is assigned to. For example livers can be formed by stem cells, simply by engineering the cells to turn to liver cells - don't know how that works exactly. So, in theory, if we are able to grow new organs from stem cells, we can solve many diseases such as heart disease, lung cancer, kidney failure, simply by replacing these organs.